Hierarchical structures composed of nodes and links can represent various decision logic. Decision logic can represent a series of decisions that divide a population into subsets. The decisions can be made on the basis of the values of one or more variables. Decision logic can be used to assign a single course of action (which could be to take no action at all) to each population subset. One example of decision logic is described in the U.S. Pat. No. 7,000,199, incorporated by reference hereto in its entirety.
Decision logic can be represented by decision tree, directed acyclic graph (“DAG”) and exception-based directed acyclic graph (“EDAG”) structures. Representations of decision logic can have leaf nodes (sometimes referred to as “action nodes”), a root node (sometimes referred to as a “start node”) and nodes that appear between the end nodes and the root nodes (sometimes referred to as “condition nodes” or “intermediate nodes” or “split nodes”). Depending on the type of a structure representing the decision logic, the root nodes, leaf nodes and intermediate nodes can be treated differently. For example, a root node can represent the beginning of an evaluation process, the intermediate nodes can represent evaluation conditions tested on one or more variables, and the leaf nodes can represent actions that should be taken if all of the evaluation steps corresponding to the condition nodes leading to these action nodes have been successfully resolved.
Decision trees can represent each of the decisions of the decision logic in a form of a branch. Decision trees can have one and only one root (or start) node. The decisions can be represented by two or more links (also referred to as “arcs”) coming out of a single node. Each branch can correspond to a set of conditions or checks that can be configured such that only one condition is true in all cases. If a condition resolves to true, a link associated with this condition can be followed further. That link can lead to either an action node (i.e., leaf node), or to another condition node. All nodes within a decision tree can have one and only one parent node.
Condition nodes of some decision trees have either a single arc to an action node or two or more arcs to condition nodes. Some decision trees can have two arcs coming out of a single condition node and leading to two action nodes. For example, two arcs coming out of a single condition node can be used to assign two actions to the two subpopulations represented by those two conditions. In some decision trees, the start node can be directly connected to a single action node. In this case, there are no branches or condition nodes at all.
Decision trees can be used for the graphical representation of complex decision logic, involving evaluations of hundreds of variables, leading to hundreds of possible outcomes. Such decision trees can require a large number of nodes that can be difficult to display and analyze.
Decision logic can also be represented by a “Directed Acyclic Graph”, or DAG. A DAG structure has a set of nodes connected by links. The decision process starts at a single root node (also referred to as a “start node”). Some DAGs can have nodes that either have a single link to an action node, or two or more links to condition nodes. Each link can go towards a node that has links coming in from other nodes. Consequently, a node within a DAG structure can have more than one parent node. DAG structures do not allow links that introduce cycles in the graph. In some DAG structures, a condition node can have a single link to another condition node.
Generally, there are two kinds of DAG's: non-backtracking and backtracking. In non-backtracking DAG's, all nodes link to a single action node, or they link to 2 or more condition nodes where the conditions of those nodes are set up so that one of them must evaluate to true. In this way, every member of the population will eventually get assigned a single action without having to revisit an earlier node to explore additional possible paths to an action.
In a backtracking DAG, it is possible for condition nodes to link to a single condition node, or to link to multiple condition nodes where more than one of those conditions can evaluate to true. Backtracking DAGs allow backtracking to earlier nodes to explore other possible paths if a certain condition node does not evaluate to true. However, the conditions of the nodes must be set up so that there is a path to an action node for every possible case from the population.
For example, a DAG can be used to represent decision logic by associating each condition node to one of the decisions in the decision logic. If the condition at that node resolves to true, then the decision process can proceed down one of its arcs. The decision process will eventually reach an action node that identifies the action assigned to that subpopulation, or another condition node that represents the next decision. If the condition at a node is false, then the decision process backs up to one of the unexplored links coming out of a node that was previously visited. The node conditions and arcs of the DAG can be set up so that it is guaranteed that exactly one action node is reached in all circumstances. Some forms of DAG structures just have a start node with a link directly to an action node, without any condition nodes in between.
Decision logic can also be represented by an Exception Directed Acyclic Graph (“EDAG”). An EDAG structure is a set of nodes connected by links. In EDAG structures, the decision process starts at a single root node called an Exception node. The Exception node represents the action to assign unless it is possible to assign some other action by following links to one of the action nodes. In some EDAG structures, each node can have only one link going out to an action node, one link going to another exception node, or one or more links going to condition nodes.
EDAG structures allow each link to go towards a node that has links coming in from other nodes. In other words, EDAG nodes can have more than one parent node. EDAG structures, just like DAG structures do not support links that introduce cycles in the graph.
An EDAG can represent decision logic, for example, by associating each condition node to one of the decisions in the decision logic. If the condition at that node resolves to true, then the decision process can proceed down one of its arcs. The decision process can either reach an action node that identifies the action assigned to that subpopulation, or it can reach another condition node that represents the next decision. If the condition at a node resolves to false, then the decision process follows one of the unexplored arcs coming out of a node that was previously visited. In some EDAG structures, the decision process may never reach an action node. In other words, EDAG structures can support subpopulations that are not expressly assigned to any particular action node. In that case, the action represented by the most recently visited exception node can be assigned to these subpopulations. One form of an EDAG structure can be represented by a single exception node.
Decision tree, DAG and EDAG structures can be leveled. A leveled decision tree can represent a structure in which all condition nodes aligned along a single column or row correspond to decisions checking the value of a single, identical variable. Similarly, a leveled DAG is a DAG (and a leveled EDAG is an EDAG) where all condition nodes correspond to decisions using the value of a single variable, and all the condition nodes corresponding to the same variable are aligned along a single column or row. In addition, the conditions on nodes, and links between nodes, can be set up so that no link goes between nodes in the same level, nor does a link go from a node in a lower level to a node in a higher level. In some DAG structures, the root node can appear in its own column or row, and all the action nodes can appear in their own column or row. In some EDAG structures, the Exception node can appear in its own column or row, and all the action nodes can appear in their own column or row.